For a full list of my publications, please visit my Google Scholar.

Topology in Phase Transitions

Phase transitions are ubiquitous. They manifest in magnets, superfluids, superconductors, liquid crystals, and countless others. Remarkably, despite appearing in such diverse contexts, they can all be understood through a single unifying framework: Landau theory. This powerful framework not only captures the physical behavior that emerges near phase transitions but also provides profound insights into the complex orders themselves.

In our recent work, we extended Landau theory by incorporating the topology of the order parameter. When thermodynamic parameters are varied in a loop, the order parameter, much like a wavefunction, can acquire a Berry phase. To illustrate this idea, we investigated the superconducting transition of an electronic system with an interaction involving two partial waves sharing the same symmetry properties. The resulting phase diagram features the thermodynamic analog of a Dirac point, which endows the gap function with its nontrivial topology. When the parameters are varied in a loop enclosing the Dirac cone, the gap function acquires a Berry phase of \(\pi\)!

Physics in Hyperbolic Space

coming soon…

Monopole Superconductivity

also coming soon…